On the Laplace transform of the Weinberg type sum rules and on the properties of pseudoscalar mesons

We reanalyse the Weinberg type sum rules in the light of the Laplace transform sum rule and including the leading non-perturbative effects. We then estimate the light quark invariant masses (hat m_s /hat m_d ,hat m_u hat m_d ) ; the pion decay amplitudef _π and theA ₁ coupling and mass. Using other type of sum rules, we derive bounds on the pseudoscalar decay amplitudesf _p (P≡π, K, D, F) as well as on the gluon component of theU(1) _A meson mass. Our main results are summarized in Sect. 4.